2017
Том 69
№ 9

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Inverse Jackson theorems in spaces with integral metric

Pichugov S. A.

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Abstract

In the spaces $L_{\Psi}(T)$ of periodic functions with metric $\rho(f, 0)_{\Psi} = \int_T \Psi(|f(x)|)dx$, where $\Psi$ is a function of the modulus-of-continuity type, we investigate the inverse Jackson theorems in the case of approximation by trigonometric polynomials. It is proved that the inverse Jackson theorem is true if and only if the lower dilation exponent of the function $\Psi$ is not equal to zero.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 3, pp 394-407.

Citation Example: Pichugov S. A. Inverse Jackson theorems in spaces with integral metric // Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 351-362.

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